Sort a linked list of 0s, 1s and 2s by changing links

• Difficulty Level : Medium
• Last Updated : 23 Jun, 2022

Given a linked list of 0s, 1s and 2s, sort it.
Examples:

```Input  : 2->1->2->1->1->2->0->1->0
Output : 0->0->1->1->1->1->2->2->2
The sorted Array is 0, 0, 1, 1, 1, 1, 2, 2, 2.

Input : 2->1->0
Output : 0->1->2
The sorted Array is 0, 1, 2```

Method 1: There is a solution discussed in below post that works by changing data of nodes.
Sort a linked list of 0s, 1s and 2s
The above solution does not work when these values have associated data with them.
For example, these three represent three colours and different types of objects associated with the colours and sort the objects (connected with a linked list) based on colours.
Method 2: In this post, a new solution is discussed that works by changing links.
Approach: Iterate through the linked list. Maintain 3 pointers named zero, one and two to point to current ending nodes of linked lists containing 0, 1, and 2 respectively. For every traversed node, we attach it to the end of its corresponding list. Finally, we link all three lists. To avoid many null checks, we use three dummy pointers zeroD, oneD and twoD that work as dummy headers of three lists.

C++

 `// CPP Program to sort a linked list 0s, 1s``// or 2s by changing links``#include ` `/* Link list node */``struct` `Node {``    ``int` `data;``    ``struct` `Node* next;``};` `Node* newNode(``int` `data);` `// Sort a linked list of 0s, 1s and 2s``// by changing pointers.``Node* sortList(Node* head)``{``    ``if` `(!head || !(head->next))``        ``return` `head;` `    ``// Create three dummy nodes to point to beginning of``    ``// three linked lists. These dummy nodes are created to``    ``// avoid many null checks.``    ``Node* zeroD = newNode(0);``    ``Node* oneD = newNode(0);``    ``Node* twoD = newNode(0);` `    ``// Initialize current pointers for three``    ``// lists and whole list.``    ``Node *zero = zeroD, *one = oneD, *two = twoD;` `    ``// Traverse list``    ``Node* curr = head;``    ``while` `(curr) {``        ``if` `(curr->data == 0) {``            ``zero->next = curr;``            ``zero = zero->next;``        ``}``        ``else` `if` `(curr->data == 1) {``            ``one->next = curr;``            ``one = one->next;``        ``}``        ``else` `{``            ``two->next = curr;``            ``two = two->next;``        ``}``        ``curr = curr->next;``    ``}` `    ``// Attach three lists``    ``zero->next = (oneD->next) ? (oneD->next) : (twoD->next);``    ``one->next = twoD->next;``    ``two->next = NULL;` `    ``// Updated head``    ``head = zeroD->next;` `    ``// Delete dummy nodes``    ``delete` `zeroD;``    ``delete` `oneD;``    ``delete` `twoD;` `    ``return` `head;``}` `// Function to create and return a node``Node* newNode(``int` `data)``{``    ``// allocating space``    ``Node* newNode = ``new` `Node;` `    ``// inserting the required data``    ``newNode->data = data;``    ``newNode->next = NULL;``}` `/* Function to print linked list */``void` `printList(``struct` `Node* node)``{``    ``while` `(node != NULL) {``        ``printf``(``"%d  "``, node->data);``        ``node = node->next;``    ``}``    ``printf``(``"\n"``);``}` `/* Driver program to test above function*/``int` `main(``void``)``{``    ``// Creating the list 1->2->4->5``    ``Node* head = newNode(1);``    ``head->next = newNode(2);``    ``head->next->next = newNode(0);``    ``head->next->next->next = newNode(1);` `    ``printf``(``"Linked List Before Sorting\n"``);``    ``printList(head);` `    ``head = sortList(head);` `    ``printf``(``"Linked List After Sorting\n"``);``    ``printList(head);` `    ``return` `0;``}` `// This code is contributed by Aditya Kumar (adityakumar129)`

C

 `// C Program to sort a linked list 0s, 1s``// or 2s by changing links``#include ``#include ` `/* Link list node */``typedef` `struct` `Node {``    ``int` `data;``    ``struct` `Node* next;``} Node;` `Node* newNode(``int` `data);` `// Sort a linked list of 0s, 1s and 2s``// by changing pointers.``Node* sortList(Node* head)``{``    ``if` `(!head || !(head->next))``        ``return` `head;` `    ``// Create three dummy nodes to point to beginning of``    ``// three linked lists. These dummy nodes are created to``    ``// avoid many null checks.``    ``Node* zeroD = newNode(0);``    ``Node* oneD = newNode(0);``    ``Node* twoD = newNode(0);` `    ``// Initialize current pointers for three``    ``// lists and whole list.``    ``Node *zero = zeroD, *one = oneD, *two = twoD;` `    ``// Traverse list``    ``Node* curr = head;``    ``while` `(curr) {``        ``if` `(curr->data == 0) {``            ``zero->next = curr;``            ``zero = zero->next;``        ``}``        ``else` `if` `(curr->data == 1) {``            ``one->next = curr;``            ``one = one->next;``        ``}``        ``else` `{``            ``two->next = curr;``            ``two = two->next;``        ``}``        ``curr = curr->next;``    ``}` `    ``// Attach three lists``    ``zero->next = (oneD->next) ? (oneD->next) : (twoD->next);``    ``one->next = twoD->next;``    ``two->next = NULL;` `    ``// Updated head``    ``head = zeroD->next;` `    ``// Delete dummy nodes``    ``free``(zeroD);``    ``free``(oneD);``    ``free``(twoD);` `    ``return` `head;``}` `// Function to create and return a node``Node* newNode(``int` `data)``{``    ``// allocating space``    ``Node* newNode = (Node*)``malloc``(``sizeof``(Node));``    ``// inserting the required data``    ``newNode->data = data;``    ``newNode->next = NULL;``}` `/* Function to print linked list */``void` `printList(``struct` `Node* node)``{``    ``while` `(node != NULL) {``        ``printf``(``"%d  "``, node->data);``        ``node = node->next;``    ``}``    ``printf``(``"\n"``);``}` `/* Driver program to test above function*/``int` `main(``void``)``{``    ``// Creating the list 1->2->4->5``    ``Node* head = newNode(1);``    ``head->next = newNode(2);``    ``head->next->next = newNode(0);``    ``head->next->next->next = newNode(1);` `    ``printf``(``"Linked List Before Sorting\n"``);``    ``printList(head);` `    ``head = sortList(head);` `    ``printf``(``"Linked List After Sorting\n"``);``    ``printList(head);` `    ``return` `0;``}` `// This code is contributed by Aditya Kumar (adityakumar129)`

Java

 `// Java Program to sort a linked list 0s, 1s``// or 2s by changing links``public` `class` `Sort012 {` `    ``// Sort a linked list of 0s, 1s and 2s``    ``// by changing pointers.``    ``public` `static` `Node sortList(Node head)``    ``{``        ``if``(head==``null` `|| head.next==``null``)``        ``{``            ``return` `head;``        ``}``        ``// Create three dummy nodes to point to``        ``// beginning of three linked lists. These``        ``// dummy nodes are created to avoid many``        ``// null checks.``        ``Node zeroD = ``new` `Node(``0``);``        ``Node oneD = ``new` `Node(``0``);``        ``Node twoD = ``new` `Node(``0``);` `        ``// Initialize current pointers for three``        ``// lists and whole list.``        ``Node zero = zeroD, one = oneD, two = twoD;``        ``// Traverse list``        ``Node curr = head;``        ``while` `(curr!=``null``)``        ``{``            ``if` `(curr.data == ``0``)``            ``{``                ``zero.next = curr;``                ``zero = zero.next;``                ``curr = curr.next;``            ``}``            ``else` `if` `(curr.data == ``1``)``            ``{``                ``one.next = curr;``                ``one = one.next;``                ``curr = curr.next;``            ``}``            ``else``            ``{``                ``two.next = curr;``                ``two = two.next;``                ``curr = curr.next;``            ``}``        ``}``        ``// Attach three lists``        ``zero.next = (oneD.next!=``null``)``? (oneD.next) : (twoD.next);``        ``one.next = twoD.next;``        ``two.next = ``null``;``        ``// Updated head``        ``head = zeroD.next;``        ``return` `head;``    ``}` `    ``// function to create and return a node``    ``public` `static` `Node newNode(``int` `data)``    ``{``        ``// allocating space``        ``Node newNode = ``new` `Node(data);``        ``newNode.next = ``null``;``        ``return` `newNode;``    ``}``  ` `    ``/* Function to print linked list */``    ``public` `static` `void` `printList(Node node)``    ``{``        ``while` `(node != ``null``)``        ``{``            ``System.out.print(node.data+``" "``);``            ``node = node.next;``        ``}``    ``}` `    ``public` `static` `void` `main(String args[]) {``        ``Node head = ``new` `Node(``1``);``        ``head.next = ``new` `Node(``2``);``        ``head.next.next = ``new` `Node(``0``);``        ``head.next.next.next = ``new` `Node(``1``);``        ``System.out.println("``Linked List Before Sorting");``        ``printList(head);``        ``head = sortList(head); ``        ``System.out.println("``\nLinked List After Sorting");``        ``printList(head);``    ``}``}` `class` `Node``{``    ``int` `data;``    ``Node next;``    ``Node(``int` `data)``    ``{``        ``this``.data=data;``    ``}``}``//This code is contributed by Gaurav Tiwari`

Python3

 `# Python3 Program to sort a linked list``# 0s, 1s or 2s by changing links``import` `math` `# Link list node``class` `Node:``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.``next` `=` `None` `#Node* newNode( data)` `# Sort a linked list of 0s, 1s and 2s``# by changing pointers.``def` `sortList(head):``    ``if` `(head ``=``=` `None` `or``        ``head.``next` `=``=` `None``):``        ``return` `head` `    ``# Create three dummy nodes to point to``    ``# beginning of three linked lists.``    ``# These dummy nodes are created to``    ``# avoid many None checks.``    ``zeroD ``=` `Node(``0``)``    ``oneD ``=` `Node(``0``)``    ``twoD ``=` `Node(``0``)` `    ``# Initialize current pointers for three``    ``# lists and whole list.``    ``zero ``=` `zeroD``    ``one ``=` `oneD``    ``two ``=` `twoD` `    ``# Traverse list``    ``curr ``=` `head``    ``while` `(curr):``        ``if` `(curr.data ``=``=` `0``):``            ``zero.``next` `=` `curr``            ``zero ``=` `zero.``next``            ``curr ``=` `curr.``next``        ``elif``(curr.data ``=``=` `1``):``            ``one.``next` `=` `curr``            ``one ``=` `one.``next``            ``curr ``=` `curr.``next``        ``else``:``            ``two.``next` `=` `curr``            ``two ``=` `two.``next``            ``curr ``=` `curr.``next``        ` `    ``# Attach three lists``    ``zero.``next` `=` `(oneD.``next``) ``if` `(oneD.``next` `) \``                            ``else` `(twoD.``next``)``    ``one.``next` `=` `twoD.``next``    ``two.``next` `=` `None` `    ``# Updated head``    ``head ``=` `zeroD.``next` `    ``# Delete dummy nodes``    ``return` `head` `# function to create and return a node``def` `newNode(data):``    ` `    ``# allocating space``    ``newNode ``=` `Node(data)` `    ``# inserting the required data``    ``newNode.data ``=` `data``    ``newNode.``next` `=` `None``    ``return` `newNode` `# Function to print linked list``def` `printList(node):``    ``while` `(node !``=` `None``):``        ``print``(node.data, end ``=` `" "``)``        ``node ``=` `node.``next``    ` `# Driver Code``if` `__name__``=``=``'__main__'``:``    ` `    ``# Creating the list 1.2.4.5``    ``head ``=` `newNode(``1``)``    ``head.``next` `=` `newNode(``2``)``    ``head.``next``.``next` `=` `newNode(``0``)``    ``head.``next``.``next``.``next` `=` `newNode(``1``)` `    ``print``(``"Linked List Before Sorting"``)``    ``printList(head)` `    ``head ``=` `sortList(head)` `    ``print``(``"\nLinked List After Sorting"``)``    ``printList(head)` `# This code is contributed by Srathore`

C#

 `// C# Program to sort a linked list 0s, 1s``// or 2s by changing links``using` `System;` `public` `class` `Sort012``{` `    ``// Sort a linked list of 0s, 1s and 2s``    ``// by changing pointers.``    ``public` `static` `Node sortList(Node head)``    ``{``        ``if``(head == ``null` `|| head.next == ``null``)``        ``{``            ``return` `head;``        ``}``        ``// Create three dummy nodes to point to``        ``// beginning of three linked lists. These``        ``// dummy nodes are created to avoid many``        ``// null checks.``        ``Node zeroD = ``new` `Node(0);``        ``Node oneD = ``new` `Node(0);``        ``Node twoD = ``new` `Node(0);` `        ``// Initialize current pointers for three``        ``// lists and whole list.``        ``Node zero = zeroD, one = oneD, two = twoD;``        ``// Traverse list``        ``Node curr = head;``        ``while` `(curr != ``null``)``        ``{``            ``if` `(curr.data == 0)``            ``{``                ``zero.next = curr;``                ``zero = zero.next;``                ``curr = curr.next;``            ``}``            ``else` `if` `(curr.data == 1)``            ``{``                ``one.next = curr;``                ``one = one.next;``                ``curr = curr.next;``            ``}``            ``else``            ``{``                ``two.next = curr;``                ``two = two.next;``                ``curr = curr.next;``            ``}``        ``}``        ` `        ``// Attach three lists``        ``zero.next = (oneD.next != ``null``)``? (oneD.next) : (twoD.next);``        ``one.next = twoD.next;``        ``two.next = ``null``;``        ` `        ``// Updated head``        ``head = zeroD.next;``        ``return` `head;``    ``}` `    ``// function to create and return a node``    ``public` `static` `Node newNode(``int` `data)``    ``{``        ``// allocating space``        ``Node newNode = ``new` `Node(data);``        ``newNode.next = ``null``;``        ``return` `newNode;``    ``}``    ` `    ``/* Function to print linked list */``    ``public` `static` `void` `printList(Node node)``    ``{``        ``while` `(node != ``null``)``        ``{``            ``Console.Write(node.data + ``" "``);``            ``node = node.next;``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``Node head = ``new` `Node(1);``        ``head.next = ``new` `Node(2);``        ``head.next.next = ``new` `Node(0);``        ``head.next.next.next = ``new` `Node(1);``        ``Console.WriteLine(``"Linked List Before Sorting"``);``        ``printList(head);``        ``head = sortList(head);``        ``Console.WriteLine(``"\nLinked List After Sorting"``);``        ``printList(head);``    ``}``}` `public` `class` `Node``{``    ``public` `int` `data;``    ``public` `Node next;``    ``public` `Node(``int` `data)``    ``{``        ``this``.data = data;``    ``}``}` `// This code is contributed by PrinciRaj1992`

Javascript

 ``

Output :

```Linked List Before Sorting
1  2  0  1
0  1  1  2  ```

Complexity Analysis:

• Time Complexity: O(n) where n is a number of nodes in linked list.
Only one traversal of the linked list is needed.
• Auxiliary Space: O(1).
As no extra space is required.

Thanks to Musarrat_123 for suggesting above solution in a comment here